verify the identity

Question

sin³x - cos³x/ sinx- cosx= 1 +(sinx)(cosx)

Answer 1

(sin³-cos³x)/(sinx-cosx)=1+(sinx)(cosx)

 

a³-b³=(a-b)(a²+ab+b²)

 

(sinx-cosx)(sin²x+sinxcosx+cos²x)/(sinx-cosx)=1+sinxcosx

divide top and bottom of the left side by (sinx-cosx)

sin²x+sinxcosx+cos²x=1+sinxcosx

sin²x+cos²x+sinxcosx=1+sinxcosx

sin²x+cos²x=1 (Pythagorean Identity)

1+sinxcosx=1+sinxcosx